Problems

On the picture below you can see graphs \(K_5\) a complete graph on \(5\) vertices and \(K_{3,3}\) a complete bipartite graph on \(3\) and \(3\) vertices. A theorem states that these graphs cannot be embedded into plane, namely one cannot draw graphs \(K_5\) and \(K_{3,3}\) on a plane in such a way that there would be no intersecting edges.
A converse statement is also true: if a graph \(G\) cannot be embedded into a plane (drawn on a plane without intersecting edges), then this graph contains either \(K_5\) or \(K_{3,3}\) as a subgraph.
The question is: can you draw the graph \(K_5\) without intersecting edges on a torus?

Is it possible to link three rings together in such a way that they cannot be separate from each other, but if you remove any ring, then the other two will fall apart?